We report experimental results on the minority of three-game, where three players choose one of two alternatives and the most rewarding alternative is the one chosen by a single player. This coordination game has many asymmetric equilibria in pure strategies that are non-strict and payoff-asymmetric and a unique symmetric mixed strategy equilibrium in which each player’s behavior is based on the toss of a fair coin. This straightforward behavior is predicted by equilibrium selection, impulse-balance equilibrium, and payoff-sampling equilibrium. Experimental participants rely on various decision rules, and only a quarter of them perfectly randomize.
Chmura, T., & Güth, W. (2011). The Minority of Three-Game: An Experimental and Theoretical Analysis. Games, 2(3), 333–354. https://doi.org/10.3390/g2030333